Mutation and the evolution of recombination

Abstract

Under the classical view, selection depends more or less directly on mutation: standing genetic variance is maintained by a balance between selection and mutation, and adaptation is fuelled by new favourable mutations. Recombination is favoured if it breaks negative associations among selected alleles, which interfere with adaptation. Such associations may be generated by negative epistasis, or by random drift (leading to the Hill-Robertson effect). Both deterministic and stochastic explanations depend primarily on the genomic mutation rate, U. This may be large enough to explain high recombination rates in some organisms, but seems unlikely to be so in general. Random drift is a more general source of negative linkage disequilibria, and can cause selection for recombination even in large populations, through the chance loss of new favourable mutations. The rate of species-wide substitutions is much too low to drive this mechanism, but local fluctuations in selection, combined with gene flow, may suffice. These arguments are illustrated by comparing the interaction between good and bad mutations at unlinked loci under the infinitesimal model.

Figure 1.

(a) The curve shows the log mean fitness as a function of the mean number of deleterious mutations. At equilibrium, this number equals U/s, where the average selection coefficient, s, is the gradient of the curve, . Therefore, if the effects of deleterious mutations are multiplicative (shown by a straight line on this log scale), the mutation load (defined as the difference in log fitness between the fittest genotype and the population mean) is L = U, as indicated at left. With negative epistasis (shown by the curve), the distance at left between the tangent and the mean fitness is still equal to U, but the mutation load, L, is much smaller. In this example, truncation selection acts on the number of deleterious mutations, with a fraction L = 0.2 surviving, and genomic mutation rate U = 10; dots indicate the equilibrium point. The population is assumed to cluster around the mean, and to be at linkage equilibrium. (b) The log mean fitness at equilibrium as a function of U, keeping genotype fitnesses the same as in (a). This decreases steeply with further increases of U.

Figure 2.

The association between a selected trait and the mutation load slows down the response to truncation selection. The upper line shows the response to truncation selection under the infinitesimal model of a trait with genetic variance at linkage equilibrium V₁ = 20; 20 per cent survive in each generation, and linkage disequilibria reduce the variance to 11.6. The lower line shows the response when truncation selection acts on the sum of this trait, and the number of deleterious mutations. Because truncation selection is spread over two traits, and because there is a correlation of 21 per cent between mutation load and the favoured trait, the selection response is substantially reduced (U = 10, as in figure 1).

Figure 3.

The different effects of a selective sweep on neutral diversity (a) and on a weakly favoured allele (b). Neutral lineages will only coalesce if they trace right back to near the origin of the sweep. Diagram (a) shows two lineages (black, grey) that both trace back into the fitter background, but both then recombine away into the ancestral background, and so remain unrelated. Such recombination, allowing the lineages to escape coalescence, can occur throughout the long time taken for the new mutation to increase from one copy (shown by disc at lower left). Diagram (b) shows how a weakly favoured allele is knocked back by a sweep. To survive, it must recombine onto the new background doing the brief duration of the sweep—giving less scope for recombination than for neutral diversity.

Figure 4.

The relation between neutral diversity, recombination rate R, and population size (small, medium, large, reading upwards), for population (a) bottlenecks, (b) deleterious mutation and (c) selective sweeps. With bottlenecks (a), diversity is independent of recombination rate, but reaches an upper limit as census numbers increase. With ‘background selection’ (b), diversity increases with recombination but is strictly proportional to census numbers. With selective sweeps (c), diversity increases to an upper limit with both population size and recombination.